{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "initial_id",
   "metadata": {
    "collapsed": true,
    "ExecuteTime": {
     "end_time": "2024-03-28T08:52:02.720646Z",
     "start_time": "2024-03-28T08:51:58.098466Z"
    }
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import random\n",
    "import torch\n",
    "from d2l import torch as d2l"
   ]
  },
  {
   "cell_type": "markdown",
   "source": [
    "### 3.2.1. 生成数据集"
   ],
   "metadata": {
    "collapsed": false
   },
   "id": "139a6525543653b1"
  },
  {
   "cell_type": "code",
   "outputs": [],
   "source": [
    "def synthetic_data(w, b, num_examples):  #@save\n",
    "    \"\"\"生成y=Xw+b+噪声\"\"\"\n",
    "    X = torch.normal(0, 1, (num_examples, len(w)))\n",
    "    y = torch.matmul(X, w) + b\n",
    "    y += torch.normal(0, 0.01, y.shape)\n",
    "    return X, y.reshape((-1, 1))\n",
    "\n",
    "true_w = torch.tensor([2, -3.4])\n",
    "true_b = 4.2\n",
    "features, labels = synthetic_data(true_w, true_b, 1000)"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-03-28T08:56:06.264941Z",
     "start_time": "2024-03-28T08:55:14.088288Z"
    }
   },
   "id": "5e2fc281cc708a6d",
   "execution_count": 4
  },
  {
   "cell_type": "code",
   "outputs": [
    {
     "data": {
      "text/plain": "(torch.Size([1000, 2]), torch.Size([1000, 1]))"
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "features.shape, labels.shape"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-03-28T08:56:17.302388Z",
     "start_time": "2024-03-28T08:56:17.286443Z"
    }
   },
   "id": "201d5a59648bec6",
   "execution_count": 5
  },
  {
   "cell_type": "code",
   "outputs": [
    {
     "data": {
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     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "d2l.set_figsize()\n",
    "d2l.plt.scatter(features[:, (1)].detach().numpy(), labels.detach().numpy(), 1);"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-03-28T08:57:30.529138Z",
     "start_time": "2024-03-28T08:57:30.307578Z"
    }
   },
   "id": "afa9552090b93ac4",
   "execution_count": 6
  },
  {
   "cell_type": "markdown",
   "source": [
    "### 3.2.2. 读取数据集"
   ],
   "metadata": {
    "collapsed": false
   },
   "id": "834c2081dc96e13c"
  },
  {
   "cell_type": "code",
   "outputs": [],
   "source": [
    "def data_iter(batch_size, features, labels):\n",
    "    num_examples = len(features)\n",
    "    indices = list(range(num_examples))\n",
    "    # 这些样本是随机读取的，没有特定的顺序\n",
    "    random.shuffle(indices)\n",
    "    for i in range(0, num_examples, batch_size):\n",
    "        batch_indices = torch.tensor(\n",
    "            indices[i: min(i + batch_size, num_examples)])\n",
    "        yield features[batch_indices], labels[batch_indices]"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-03-28T09:02:54.848397Z",
     "start_time": "2024-03-28T09:02:54.829032Z"
    }
   },
   "id": "129e0a0d3d5b8b58",
   "execution_count": 12
  },
  {
   "cell_type": "code",
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([[-0.9765,  0.8705],\n",
      "        [ 0.0291, -0.0952],\n",
      "        [-0.3574,  0.7945],\n",
      "        [ 0.6716,  0.4245],\n",
      "        [-0.4873, -0.5797],\n",
      "        [-0.2081,  0.3100],\n",
      "        [ 0.3301,  0.4063],\n",
      "        [-0.4239,  1.7862],\n",
      "        [-0.3300, -1.5522],\n",
      "        [ 0.1346,  1.1731]]) \n",
      " tensor([[-0.7249],\n",
      "        [ 4.5859],\n",
      "        [ 0.7800],\n",
      "        [ 4.1024],\n",
      "        [ 5.1916],\n",
      "        [ 2.7357],\n",
      "        [ 3.4993],\n",
      "        [-2.7204],\n",
      "        [ 8.8177],\n",
      "        [ 0.4991]])\n"
     ]
    }
   ],
   "source": [
    "batch_size = 10\n",
    "\n",
    "for X, y in data_iter(batch_size, features, labels):\n",
    "    print(X, '\\n', y)\n",
    "    break"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-03-28T09:02:55.425855Z",
     "start_time": "2024-03-28T09:02:55.409796Z"
    }
   },
   "id": "355630ac3b9d06d4",
   "execution_count": 13
  },
  {
   "cell_type": "markdown",
   "source": [
    "### 3.2.3. 初始化模型参数"
   ],
   "metadata": {
    "collapsed": false
   },
   "id": "cde414bc9b0bbea3"
  },
  {
   "cell_type": "code",
   "outputs": [],
   "source": [
    "w = torch.normal(0, 0.01, size=(2,1), requires_grad=True)\n",
    "b = torch.zeros(1, requires_grad=True)"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-03-28T09:03:29.001231Z",
     "start_time": "2024-03-28T09:03:28.989726Z"
    }
   },
   "id": "9026baff5be0f40b",
   "execution_count": 14
  },
  {
   "cell_type": "markdown",
   "source": [
    "### 3.2.4. 定义模型"
   ],
   "metadata": {
    "collapsed": false
   },
   "id": "4bf71db01b2d0278"
  },
  {
   "cell_type": "code",
   "outputs": [],
   "source": [
    "def linreg(X, w, b):  #@save\n",
    "    \"\"\"线性回归模型\"\"\"\n",
    "    return torch.matmul(X, w) + b"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-03-28T09:04:27.656674Z",
     "start_time": "2024-03-28T09:04:27.645625Z"
    }
   },
   "id": "62bbd7f47dc3b78e",
   "execution_count": 16
  },
  {
   "cell_type": "markdown",
   "source": [
    "### 3.2.5. 定义损失函数"
   ],
   "metadata": {
    "collapsed": false
   },
   "id": "cf2c65a49b8c4d84"
  },
  {
   "cell_type": "code",
   "outputs": [],
   "source": [
    "def squared_loss(y_hat, y):  #@save\n",
    "    \"\"\"均方损失\"\"\"\n",
    "    return (y_hat - y.reshape(y_hat.shape)) ** 2 / 2"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-03-28T09:04:49.405631Z",
     "start_time": "2024-03-28T09:04:49.386579Z"
    }
   },
   "id": "22a2984bfedff95a",
   "execution_count": 17
  },
  {
   "cell_type": "markdown",
   "source": [
    "### 3.2.6. 定义优化算法"
   ],
   "metadata": {
    "collapsed": false
   },
   "id": "17f42ec0fd0848d1"
  },
  {
   "cell_type": "code",
   "outputs": [],
   "source": [
    "def sgd(params, lr, batch_size):  #@save\n",
    "    \"\"\"小批量随机梯度下降\"\"\"\n",
    "    with torch.no_grad():\n",
    "        for param in params:\n",
    "            param -= lr * param.grad / batch_size\n",
    "            param.grad.zero_()"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-03-28T09:05:42.658566Z",
     "start_time": "2024-03-28T09:05:42.641030Z"
    }
   },
   "id": "98639097735d4187",
   "execution_count": 18
  },
  {
   "cell_type": "markdown",
   "source": [
    "### 3.2.7. 训练"
   ],
   "metadata": {
    "collapsed": false
   },
   "id": "eaf6a08ff188cf54"
  },
  {
   "cell_type": "code",
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch 1, loss 0.000051\n",
      "epoch 2, loss 0.000050\n",
      "epoch 3, loss 0.000050\n"
     ]
    }
   ],
   "source": [
    "lr = 0.03\n",
    "num_epochs = 3\n",
    "net = linreg\n",
    "loss = squared_loss\n",
    "\n",
    "for epoch in range(num_epochs):\n",
    "    for X, y in data_iter(batch_size, features, labels):\n",
    "        l = loss(net(X, w, b), y)\n",
    "        l.sum().backward()\n",
    "        sgd([w, b], lr, batch_size)\n",
    "    with torch.no_grad():\n",
    "        train_l = loss(net(features, w, b), labels)\n",
    "        print(f'epoch {epoch + 1}, loss {float(train_l.mean()):f}')"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-03-28T09:18:07.394373Z",
     "start_time": "2024-03-28T09:18:07.261287Z"
    }
   },
   "id": "c36d98c5102913b8",
   "execution_count": 24
  },
  {
   "cell_type": "code",
   "outputs": [
    {
     "data": {
      "text/plain": "(tensor([[ 1.9996],\n         [-3.4003]], requires_grad=True),\n tensor([4.1996], requires_grad=True))"
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "w, b"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-03-28T09:18:16.583353Z",
     "start_time": "2024-03-28T09:18:16.561286Z"
    }
   },
   "id": "6cd53d24a9494c9",
   "execution_count": 25
  },
  {
   "cell_type": "code",
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "w的估计误差: tensor([0.0004, 0.0003], grad_fn=<SubBackward0>)\n",
      "b的估计误差: tensor([0.0004], grad_fn=<RsubBackward1>)\n"
     ]
    }
   ],
   "source": [
    "print(f'w的估计误差: {true_w - w.reshape(true_w.shape)}')\n",
    "print(f'b的估计误差: {true_b - b}')"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-03-28T09:21:54.127985Z",
     "start_time": "2024-03-28T09:21:54.111698Z"
    }
   },
   "id": "f0d5d3338eff55c7",
   "execution_count": 26
  },
  {
   "cell_type": "code",
   "outputs": [],
   "source": [],
   "metadata": {
    "collapsed": false
   },
   "id": "8f47ca6dce120935"
  }
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